Hello, yes, it's me, Matisguy. This episode is not part of the story, in case that wasn't obvious. This is mostly me just posting materials I made for the SciFi here while it still has my interest and imagination. In particular, I spent way too long thinking through just how exactly the Lifting Rocket would actually work, and want to convince myself that it wasn't all just a waste of creative energy on details that don't really matter. Sooooo...
The basic schematic in my head for the Fusion Rocket is pictured below. The idea is, Hot Hydrogen (mostly Tritium) pumped up the Space Elevator is to be ionized by interaction with the conductive pipe walls, which themselves are kept at very high positive voltage relative to Space. The Ions are then accelerated via a normal Linear Particle Accelerator wrapped around the tube (probably only near the end of the Elevator, due to limitations on power transmission from the Fusion Chamber), to a precise velocity common to all the types of Ion, near Lightspeed. They are then injected into the Chamber as such:
Within the Center of the Chamber is a rotating Magnetic Field and rotating Electric Field, both of which are perpendicular to and rotating around the axis through which the Ion were initially injected. These strongly deflect the Ions away from their original path. Tritons and Singly-Ionized alpha particles are simply ejected from the Rocket as propellant. Deuterons and Doubly Ionized Alpha Particles, however, are to be trapped going around a loop in the Fusion Chamber. The fields in the center of the Chamber alone are insufficient to achieve this; however, there are also to be rotating fields nearer to the chamber's inner walls, 180 degrees out phase with the fields in the center of the Chamber, and moreover the rotation rate of the fields are to match that of the deuterons around their travel loop. In particular, this means the deuteron oscillation resonates with the cylindrical chamber's 2nd harmonic mode. Further, while in the center of the Chamber the Electric deflection opposes the Magnetic Deflection, the Electric and Magnetic fields are both to deflect the deuteron back towards the chamber center together when nearer the walls, making for more efficient confinement despite the weaker field amplitude near the walls.
Thus, a dense halo of high-energy deuterons should appear within the Fusion Chamber quickly, leaving and re-entering the Fusion Area constantly, once each period for each arc of the cylinder. The Chamber Center should thus eventually become a very hot, dense, high-pressure beam of upward-moving deuterons and tritons; conditions should be right for Fusion to ignite as such.
Each Fusion event produces a doubly-ionized alpha particle, a neutron, and about 18 MegaElectronVolts (read: huge amounts) of energy. The doubly-ionized alpha particles have almost exactly the same charge-to-mass ratio as the deuterons, and thus become trapped in the halo with them after production. They are also much more electronegative than either the tritons or deuterons, and hence are most likely to bond with any electrons that migrate to the positive-ion beam; when they do, they become singly-ionized and are ejected as exhaust. This, plus the Triton ejection, and small contributions from the electron gun and radiation pressure, is ultimately what generates Thrust; what ultimately generates Power is the acceleration of the alpha particles by a Fusion event. The energy added to the alpha particles by said event is captured by the halo, transmitted to the Rotating Electromagnetic Fields and Harmonic Mode, and then eventually to the walls around the chamber, which convert it to useful power for the Ship and Elevator.
I've also overengineered the Fusion Chamber's walls, by the way. The outlined bit in the schematic above is zoomed in on here:
Not shown are items such as coolant pipes, the details of how exactly the diodes and resonator coils interact and pack together, and the details of the resonator winding. They are, uh, left as exercises for the reader. It should be mentioned, though, that the neutron window is slightly different from the rest of the chamber walls; it uses tritide because such scatters neutrons instead of absorbing them (useful for cooling the Lithium in the Radiator), and it also has some shielding for the event that non-ionized particles are blown up from the fuel pipe. Said particles then just escape through the exhaust outlets through normal aerodynamics.
It should also be said that the "Electron Guns" forming a ring around the bottom of the ship are essentially just lightning rods forced to work in reverse. Even small applied voltages generate high electrostatic fields at their tip, which then draws and accelerates electrons out into the vacuum of space (probably to then mingle with the ion exhaust). The only truly unusual thing about them is how much continuous current they're made to handle when the resonators and photodiodes from the ship are powered.
Speaking of electrostatics, the very last image I've made for this was an attempt to convince myself that a chamber shaped as above actually can in fact contain a positively charged plasma without melting from wall contact, bearing in mind that electrically conductive walls form an equipotential surface. If it were simply a cylindrical tube it'd be no problem, but the floor and ceiling make it difficult. Honestly, looking at it makes obvious another good reason for the positive DC bias to be so absurdly strong.
Well, that's all I've got. You may now spam the nerd emoji in the comments of this episode.
Have a nice life!
EDIT: Decided to also try and visualize the Poynting Vectors of the Resonant Cavity Mode. For those who don't know, these vectors represent the Momentum stored in an Electromagnetic Field, point in the direction of Energy Flow, and are perpendicular to a charged particle's acceleration/deflection due to those fields. In quantum mechanical contexts they also show the direction/intensity of Photon Travel. Ions will exchange their energy and momentum with these Fields and vice versa, especially if they resonate.
I've guesstimated the Poynting vectors above in the absence of the Electrostatic Field in the chamber, and also without the effect of the Fusing Ions on it (This is why it's divergence free outside the walls). The Deuteron Loops should end up trapped in the lower curling regions that oppose their motion, and when Fusion is active the Poynting vectors should generally point more strongly away from the Fusion Area. With or without fusion, the effect of the ions and electrostatic potential together should be to point the Vectors more strongly towards the exhaust ports and out of the Chamber, providing thrust.
EDIT 2: Decided to figure out what the configuration of the electron guns and chamber dimensions should probably be in more detail. I've also added a static magnetic field to the design to help the resonance along, and realized that the Particle Accelerator can be made to distinguish between the tritons and deuterons by their charge-mass ratio; this is useful for splitting energy evenly between the particles and necessitates them entering the chamber with slightly different frequencies. As a matter of fact, all the electron guns and ion emitters are to eject such at particular frequencies now, and will be directly connected to the associated resonators to accomplish as much. In particular, the set of electron guns inside the Fusion Chamber itself are necessary to partially neutralize the ion gas so electrostatic potential does not build indefinitely in there; they also allow for effective AC current to flow along the axis of the chamber and create a beam of electrons that even more strongly confines the ion gas in the chamber (the electrons themselves are strongly constrained to lie along the chamber axis by the magnetic field).
Each electron gun of its kind is captioned with its emitting frequency. The multiplicative factors in the table of lengths are derived from the roots of the Bessel Functions; in particular L(x,y) is the yth root of the xth Bessel Function multiplied by the scale factor. These are the radial solutions for the resonant modes of a cylindrical cavity, such as the Fusion Chamber.
Finally, some thoughts on how efficient this rocket is: in theory, as a heat engine, it should be approximated by the Carnot cycle. Fusion only occurs at a specific temperature, and Work is extracted from and done directly on the ions involved, adiabatically. The inlet/outlet of fuel completes the cycle. In theory, this should be an extremely efficient process that produces very little waste heat compared to the overall work done, and most of said waste heat should simply escape to space. In actuality, though, I expect losses to electrical resistance and non-resonant radiative modes (particularly atomic Bremsstrahlung, which is an awesome word) to throw away much more heat than the theoretical minimum. I don't think it'd be enough to melt the rocket or anything, especially given how little fuel is actually needed to generate substantial thrust, but the theoretical 99.999% Carnot efficiency between the heat source and sink is probably much too generous.
...Also, to be more candid, I have Nerd Sniped myself badly over this. Maybe NASA will find this all useful one day?
